After excluding 409 participants with missing data, participants with a complete depression variable (29,977 of 30,386; 98.7%) were included in the final analysis. We found the results showing no significant changes in most cases, before and after exclusion (Additional file 1 Sensitivity analysis on the effect of included and censored the excluding participants on the overall results).

Socio-demographic characteristics

Of the 29,977 students (Table 1), more than half were male (53.1%), and with a medium family economic level (63.2%). Nearly half (42.6%) of the students were in grades 7–9. Most of the students reported paternal (61.2%) and maternal (56.5%) education levels to be “middle school”. 15.6% of students reported their parents divorced, remarried, or died; 65.2% reported left-behind experience; 8.2% reported bullying victimization experience; and 17.0% reported self-harm behavior.

Table 1 Sociodemographic characteristics and mental health conditions with depression and suicidal ideation (N = 29,977)Depression and suicidal ideation

Among all the students (Table 1), 20.2% scored more than 9 points in depression, and 24.2% reported suicidal ideation. Higher depression scores and suicidal ideation are associated with a higher proportion of parents divorced, remarried, or died, and more experiences of being left behind, being bullied, or engaging in self-harm behavior (ps < 0.05).

Cooccurrence of unfavorable parental marital status, left-behind experience, bullying victimization, and self-harm behavior

Overall (Table 1), more than three-quarters of the students (75.3%) reported at least one of the four syndemic conditions, namely unfavorable parental marital status, left-behind experience, bullying victimization, or self-harm behavior. Nearly a quarter of students (24.8%) reported at least two syndemic conditions. Students with high depression scores or suicidal ideation reported significantly more types of syndemic conditions (ps < 0.05).

Multivariable logistic regression analyses among intersecting health problems

Table 2 presents the multivariable logistic regression models of the four vulnerable conditions with depression and suicidal ideation. Left-behind experience (aOR = 1.65; 95% CI = 1.52–1.79), being bullied (aOR = 1.32; 95% CI = 1.17–1.49), self-harm behavior (aOR = 1.18; 95% CI = 1.07–1.31), depression (aOR = 1.20; 95% CI = 1.09–1.33), and suicidal ideation (aOR = 1.20; 95% CI = 1.08–1.32) were significantly associated with higher odds of students’ parents divorced, remarried, or died.

Table 2 Multivariable logistic regression analyses of unfavorable parental marital status, left-behind experience, bullying victimization, self-harm behavior, depression, and suicidal ideation (N = 29,977)

The odds of parents divorced, remarried, or died (aOR = 1.65; 95% CI = 1.52–1.79), and depression (aOR = 1.14; 95% CI = 1.05–1.23) were significantly associated with higher odds of left-behind experience.

Higher odds of experiencing bullying were significantly associated with having divorced, remarried, or died parents (aOR = 1.34; 95% CI = 1.19–1.51), having self-harm behavior (aOR = 1.90; 95% CI = 1.69–2.13), depression (aOR = 2.37; 95%CI = 2.10–2.67), and suicidal ideation (aOR = 1.96; 95% CI = 1.73–2.21).

The experience of being bullied (aOR = 1.96; 95% CI = 1.74–2.19), parents divorced, remarried, or died (aOR = 1.19; 95% CI = 1.07–1.31), depression (aOR = 2.89; 95% CI = 2.65–3.15), and suicidal ideation (aOR = 6.80; 95% CI = 6.25–7.40) were significantly associated with higher odds of self-harm behavior.

Experience of divorced, remarried, or died parents (aOR = 1.20; 95% CI = 1.09–1.33), being left-behind (aOR = 1.14; 95% CI = 1.05–1.24), being bullied (aOR = 2.44; 95% CI = 2.16–2.75), self-harm behavior (aOR = 2.92; 95% CI = 2.67–3.18), and suicidal ideation (aOR = 9.70; 95% CI = 8.97–10.49) were significantly associated with higher odds of depression.

Experiencing parents divorced, remarried, or died (aOR = 1.19; 95% CI = 1.08–1.32), being bullied (aOR = 1.93; 95% CI = 1.71–2.17), having self-harm behavior (aOR = 6.80; 95% CI = 6.25–7.40), and depression (aOR = 9.68; 95% CI = 8.95–10.47) were significantly associated with higher odds of suicidal ideation.

Cumulative effects of unfavorable parental marital status, left-behind experience, bullying victimization, and self-harm behavior on depression and suicidal ideation

Table 3 shows the results of multivariable logistic regression models of the association between each vulnerable condition and the two outcome measures, and the cumulative effects of all vulnerable conditions on depression and suicidal ideation. There was a significant trend in the relationship between the number of syndemic conditions ranging from 0 to 4 and the proportions of depression and suicidal ideation, such that as every one-unit increase in the number of syndemic conditions, the odds of being depressed and having suicidal ideation increased significantly. Specifically, compared to students without any vulnerable conditions, those with one, two, three, or four syndemic conditions were significantly more likely to suffer from depression: (aOR = 1.61; 95% CI = 1.74–1.77), (aOR = 4.68; 95% CI = 4.24–5.18), (aOR = 13.98; 95% CI = 12.08–16.19), (aOR = 29.68; 95% CI = 19.77–44.56). Similarly, compared to students without any vulnerable conditions, those with one, two, three, or four syndemic conditions were significantly more likely to have suicidal ideation: (aOR = 1.60; 95% CI = 1.47–1.75), (aOR = 5.30; 95% CI = 4.83–5.82), (aOR = 15.87; 95% CI = 13.71–18.38), (aOR = 30.46; 95% CI = 19.64–47.25).

Table 3 Multivariable logistic regression models of cumulative effects of four syndemic factors on depression and suicidal ideationModel of synergistically interacting epidemicsDepression

We used multivariable logistic regression models with product terms to estimate a multiplicative interaction for vulnerable conditions on depression (Table 4).

Table 4 Multiplicative two-/three-way interactions of syndemic factors on depression and suicidal ideation

We estimated a multiplicative interaction between every two vulnerable conditions. In the two-way interactions, the joint effects of unfavorable parental marital status with left-behind experience (model 1: aOR = 1.54, 95% CI: 1.40–1.69), unfavorable parental marital status with bullying victimization (model 2: aOR = 4.80, 95% CI: 3.93–5.87), unfavorable parental marital status with self-harm behavior (model 3: aOR = 6.97, 95% CI: 6.01–8.09), left-behind experience with bullying victimization (model 4: aOR = 4.23, 95% CI: 3.77–4.74), left-behind experience with self-harm behavior (model 5: aOR = 7.05, 95% CI: 6.49–7.66), and bullying victimization with self-harm behavior (model 6: aOR = 12.45, 95% CI: 10.62–14.59) were associated with depression.

In the logistic regression model including all two-way product terms and adjusting for gender, grade, family economic status, and paternal/maternal education level (model 7 in Table 4), we found multiplicative interactions for joint effects of unfavorable parental marital status with bullying victimization (aOR = 1.66, 95% CI: 1.25–2.21), unfavorable parental marital status and self-harm behavior (aOR = 2.22, 95% CI: 1.83–2.68), left-behind experience and bullying victimization (aOR = 1.53, 95% CI:1.30–1.81), left-behind experience and self-harm behavior (aOR = 4.84, 95% CI: 4.41–5.30), and bullying victimization and self-harm behavior (aOR = 3.65, 95% CI: 2.99–4.46) on depression. We found that the joint effects of unfavorable parental marital status and left-behind experience acted as a protective factor (aOR = 0.88, 95% CI: 0.77–0.99) on depression.

In sum, by examining synergistic effects, we found that any two vulnerable conditions - unfavorable parental marital status and left-behind experience, unfavorable parental marital status and bullying victimization, unfavorable parental marital status and self-harm behavior, left-behind experience and bullying victimization, left-behind experience and self-harm behavior, bullying victimization and self-harm behavior - were associated with depression when they co-occurred.

In the three-way interactions, the joint effects of unfavorable parental marital status with left-behind experience with bullying victimization (model 8: aOR = 4.74, 95% CI: 3.77–5.97), unfavorable parental marital status with left-behind experience with self-harm behavior (model 9: aOR = 6.79, 95% CI: 5.73–8.04), unfavorable parental marital status with bullying victimization with self-harm behavior (model 10: aOR = 13.94, 95% CI: 9.81–19.81), and left-behind experience with bullying victimization with self-harm behavior (model 11: aOR = 11.87, 95%CI: 9.83–14.34) were associated with depression.

In a regression model that includes all three-way product terms, we found multiplicative interaction for joint effects of unfavorable parental marital status and left-behind experience and self-harm behavior (aOR = 4.383, 95%CI: 4.02–5.79), and left-behind experience and bullying victimization and self-harm behavior (aOR = 8.96, 95%CI: 7.33–10.96) on depression.

When exploring the synergistic effects of three-way interactions, the interactions between any three vulnerable conditions - unfavorable parental marital status and left-behind experience and bullying victimization, unfavorable parental marital status and left-behind experience and self-harm behavior, unfavorable parental marital status and bullying victimization and self-harm behavior, left-behind experience and bullying victimization and self-harm behavior - were all associated with depression.

Suicidal ideation

Table 4 shows logistic regression models with product terms to assess the multiplicative effects of vulnerable conditions on suicidal ideation.

We found the joint effects of unfavorable parental marital status with left-behind experience (model 1: aOR = 1.47, 95% CI: 1.34–1.60), unfavorable parental marital status with bullying victimization (model 2: aOR = 4.05, 95% CI: 3.33–4.94), unfavorable parental marital status with self-harm behavior (model 3: aOR = 8.61, 95% CI: 7.34–10.09), left-behind experience with bullying victimization (model 4: aOR = 3.91, 95% CI: 3.50–4.37), left-behind experience with self-harm behavior (model 5: aOR = 9.87, 95% CI: 9.06–10.75), and bullying victimization with self-harm behavior (model 6: aOR = 15.20, 95% CI: 12.75–18.13) on suicidal ideation.

In a logistic regression model including all two-way product terms and controlling for sociodemographic factors (model 7 in Table 4), we found multiplicative interactions for joint effects of unfavorable parental marital status and bullying victimization (aOR = 1.52, 95% CI: 1.14–2.03), unfavorable parental marital status and self-harm behavior (aOR = 2.40, 95% CI: 1.97–2.93), left-behind experience and bullying victimization (aOR = 1.52, 95% CI: 1.29–1.78), left-behind experience and self-harm behavior (aOR = 6.96, 95% CI: 6.34–7.64), and bullying victimization and self-harm behavior (aOR = 4.47, 95% CI: 3.62–5.52) on suicidal ideation. The joint effects of unfavorable parental marital status and left-behind experience acted as a protective factor (aOR = 0.84, 95% CI: 0.74–0.94) on suicidal ideation.

The joint effects of unfavorable parental marital status with left-behind experience with bullying victimization (model 8: aOR = 3.92, 95% CI: 3.13–4.92), unfavorable parental marital status with left-behind experience with self-harm behavior (model 9: aOR = 8.45, 95% CI: 7.05–10.13), unfavorable parental marital status with bullying victimization with self-harm behavior (model 10: aOR = 13.02, 95% CI: 8.95–18.92), and left-behind experience with bullying victimization with self-harm behavior (model 11: aOR = 14.41, 95% CI: 11.69–17.78) were associated with suicidal ideation.

In model 12, We found the joint effects of unfavorable parental marital status and left-behind experience and self-harm behavior (aOR = 6.35, 95% CI: 5.25–7.68), and left-behind experience and bullying victimization and self-harm behavior (aOR = 11.25, 95% CI: 9.05–13.98) on suicidal ideation, adjusting for sociodemographic factors.

Overall, two-way interactions and three-way interactions with suicidal ideation were found to have the same results as depression in this study.